Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x-3y &= -3 \\ 5x+5y &= 9\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = -5y+9$ Divide both sides by $5$ to isolate $x$ $x = {-y + \dfrac{9}{5}}$ Substitute this expression for $x$ in the first equation. $-6({-y + \dfrac{9}{5}}) - 3y = -3$ $6y - \dfrac{54}{5} - 3y = -3$ Simplify by combining terms, then solve for $y$ $3y - \dfrac{54}{5} = -3$ $3y = \dfrac{39}{5}$ $y = \dfrac{13}{5}$ Substitute $\dfrac{13}{5}$ for $y$ in the top equation. $-6x-3( \dfrac{13}{5}) = -3$ $-6x-\dfrac{39}{5} = -3$ $-6x = \dfrac{24}{5}$ $x = -\dfrac{4}{5}$ The solution is $\enspace x = -\dfrac{4}{5}, \enspace y = \dfrac{13}{5}$.